Differential and Integral Equations

Positive solution branch for elliptic problems with critical indefinite nonlinearity

Jacques Giacomoni, J. Prajapat, and Mythily Ramaswamy

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In this paper, we study the semilinear elliptic problem with critical nonlinearity and an indefinite weight function, namely $- \Delta u =\lambda u + h (x) u^{\frac{n+2}{n-2}} $ in a smooth domain bounded (respectively, unbounded) $\Omega\subseteq\,\mathbb R^n , \ n > 4 $, for $\lambda \geq 0 $. Under suitable assumptions on the weight function, we obtain the positive solution branch, bifurcating from the first eigenvalue $\lambda_1(\Omega)$ (respectively, the bottom of the essential spectrum).

Article information

Differential Integral Equations, Volume 18, Number 7 (2005), 721-764.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J65: Nonlinear boundary value problems for linear elliptic equations
Secondary: 35B33: Critical exponents 35J25: Boundary value problems for second-order elliptic equations 47J15: Abstract bifurcation theory [See also 34C23, 37Gxx, 58E07, 58E09] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Giacomoni, Jacques; Prajapat, J.; Ramaswamy, Mythily. Positive solution branch for elliptic problems with critical indefinite nonlinearity. Differential Integral Equations 18 (2005), no. 7, 721--764. https://projecteuclid.org/euclid.die/1356060164

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